METHOD FOR CONTROLLING THE AUTOMATIC ROLLING OF PIPES IN A REELING MILL

Description

[0001] The present invention relates to a method for controlling the automatic rolling of pipes in a reeling mill. More particularly, the invention relates to a method for automatically controlling the screwing-down of rolls in the process of reeling in the production of seamless steel pipes by the Mannesmann plug mill method.

[0002] The reeling mill (reeler) is layed between the plug mill and sizing mill in the process for manufacture of seamless steel pipes. In this mill, the pipe is "reeled" by reducing its wall thickness for various purposes among which are the correction of the thickness deviation that has developed in the previous rolling mills (i.e. piercer, elongator and plug mill), elimination of the flaws developed by abrasion with the plug in the plug mill rolling, and ensuring a suitable amount of pipe expansion for the sizing mill in the subsequent step. It is the most important feature of the reeling mill that the greater part of the amount of reduction in wall thickness changes into the expansion of the outside diameter of the pipe, so if a variation occurs in the amount of reduction of the wall thickness during reeling, the outside diameter of the reeled pipe also changes in its longitudinal direction and the following disadvantages result: if the amount of reduction in wall thickness during reeling is small, the degree of increase in the outside diameter is small and the desired outside diameter of the pipe cannot be achieved, and vice versa. If the outside diameter of the reeled pipe is smaller than a predetermined value, not all part of the pipe is rolled in the subsequent sizing mill, which has a very adverse effect on the outside diameter of the final product. If the outside diameter of the reeled pipe is larger than the predetermined value, a flaw such as one due to the roll edges develops during rolling in the sizing mill, which is also detrimental to the quality of the final product. So, the operation in the reeling mill has great effect on the accuracy of the dimensions of the final product, hence its yield, and it is mandatory in the reeling mill to roll the pipe to have the desired outside diameter.

[0003] -Several methods are known for controlling the operation of reeling mills. One of them is described in JP-A-37568/78, and to provide a pipe of constant outside diameter on the leaving side of the mill, in this method the electric power for rolling is kept constant for each lot and for the entire length of each pipe to be rolled. Another method is described in JP-A-86663/78, and to provide a pipe of constant wall thickness on the leaving side, the pattern of electrical power outputs is determined for each pipe on the basis of information of the cross section and temperature of the pipe on the entry side so that the cross section of the pipe on the leaving side is kept constant for each lot and for the entire length of each pipe, and the electric power for rolling is changed after this pattern.

[0004] The method of JP-A-37568/78 disregards the change in the temperature of each pipe to be rolled as well as the change in the temperature in the longitudinal direction of the pipe. So, if the reeling operation is performed with the electric power held constant, the reduction in the wall thickness at the low temperature portion of pipe where occurs the larger resistance to deformation is so small that the pipe on the leaving side cannot be expanded to the predetermined value of outside diameter. What is more, the outside diameter of the pipe on the entry side of the mill is alsovaried in longitudinal direction by the rolling force and by the set of roll gap in the plug mill rolling, so this adds to the variation in the outside diameter of the pipe that is leaving the reeling mill under the control of constant electric power.

[0005] The method of JP-A-8666378 achieves its object by changing the desired electric power according to a predetermined pattern by taking into account the change in the temperature of the pipe in its longitudinal direction, but as in the first method, it disregards the change in the outside diameter of the pipe on the entry side in defining the target value for the electric power that provides a pipe of constant cross-sectional area on the leaving side of the mill. As a result, there occurs a variation in the outside diameter of the reeled pipe both in the longitudinal direction and with respect to the average outside diameter of the pipes for each lot. The second method has another defect: the pipe to be fed into the plug mill generally has such a temperature distribution in the longitudinal direction that the temperature increases from the leading end to the trailing end, and so the wall thickness of the pipe leaving the plug mill often increases from the leading end to the trailing end. Therefore, the pipe entering the reeling mill generally has a cross section that decreases from the leading end to the trailing end.

[0006] To reel the pipe having a cross-sectional area of the pattern described above and provide a product whose cross section is uniform in the longitudinal direction, the amount of reduction in wall thickness must be decreased from the leading to trailing edge, but then, the resulting pipe on the leaving side has an outside diameter that decreases from the leading to trailing end and which is not desired in the final product. Still another defect that is common to the two methods is that in spite of the supply of a constant electric power for rolling, a change in the speed of the rolling motor during reeling causes a change in the rolling torque, and as a result, the desired outside diameter is not attained.

[0007] Finally, JP-A-50,907180 discloses a method for screwing-down of reeling rolls in a reeling mill, and its object is to provide a method for producing a sizing tube blank to be finished into a seamless tube product with a constant outer diameter and wall thickness being set as the aim values. In this known method the reeling mill tube blank is reeled such that the aim value in the outer diameter of the sizing tube blank delivered from the plug mill is not set to be constant, but the aim value of the sizing tube blank is to be altered according to the deviation data of the wall thickness of the reeling mill tube blank.

[0008] It is an object of the present invention to provide a control method for screwing down the reeling rolls that is free from the above described defects of the conventional techniques and which enables a quantitative adjustment of the roll gap so that a pipe leaving the reeling mill has a uniform outside diameter in the longitudinal direction.

[0009] The present invention provides a method for controlling the automatic rolling pipes in a reeling mill comprising the steps of: determining an aimed amount of reduction in wall thickness of said pipe being reeled, continuously monitoring the voltage and current supplied to a rolling motor of the reeling mill, generating correction signals based upon the aimed reduction, continuously monitoring the speed of said rolling motor, and adjusting the screwing-down of reeling rolls in response to said correction signals, said method being characterized by calculating the torque of said rolling motor by a predetermined mathematical relationship of the voltage, the current and the speed of said rolling motor, measuring the temperature of said pipe on the entry side of said reeling mill, directly measuring the outside diameter of the pipe supplied to said reeling mill, directly measuring the wall thickness of said pipe supplied to said reeling mill, calculating the estimated actual reduction in wall thickness based upon a predetermined relationship of said temperatures and said torque, and generating said correction signals based upon the relationship between the aimed reduction and said calculated actual reduction.

[0010] Main steps of this method reside in first determining the desired amount of reduction in wall thickness in the longitudinal direction of the pipe being reeled, then calculating the actual amount of reduction in wall thickness from the torque of the rolling motor and the temperature of the pipe on the entry side and finally controlling said actual amount of reduction in wall thickness to be equal to the desired amount of reduction in wall thickness.

[0011] Thus, in the present invention the desired amount of reduction in the wall thickness of the pipe being reeled is determined for the longitudinal direction of the pipe from the outside diameter and average wall thickness of the pipe on the entry side of the reeling mill and the desired outside diameter of the pipe on the leaving side, the actual amount of reduction in the wall thickness of the pipe being reeled is calculated for the longitudinal direction of the pipe from the temperature of the pipe on the entry side of the reeling mill and the rolling torque of the rolling motor, and the degree of screwing down the reeling rolls is controlled so that the actual amount of reduction in wall thickness is equal to said desired amount of reduction in wall thickness.

[0012] A control apparatus for screwing down reeling rolls includes a wall thickness and OD arithmetic means for calculating the average wall thickness and the outside diameter of a pipe being fed into the reeling rolls, an AGC means which receives information on said average wall thickness and outside diameter of the pipe on the entry side of the reeling mill, the temperature of the pipe on the entry side of the reeling mill; the voltage and current applied to the armature of a rolling motor, the speed of rotation of the motor, and the desired outside diameter of the pipe on the leaving side of the mill, and calculates the desired amount of reduction in wall thickness and the actual amount of reduction in the wall thickness of the pipe being rolled to thereby deliver a signal indicative of the difference between the desired amount of reduction in wall thickness and the actual amount of reduction in wall thickness, and a screw down motor control means that delivers a screw down signal to a screw down motor in rsponse to a difference signal. The AGC means as used herein means an "automatic roll gap control means" which delivers a signal indicative of the difference between the desired amount of reduction in wall thickness and the actual amount of reduction in wall thickness to the screw down motor control means for driving the motor.

[0013] The invention will be more fully understood from the following description when taken in conjunction with the drawings, in which:

Figure 1 is a block diagram showing the control system as used in a reeling mill;

Figure 2 shows schematically a cross section of a pipe being rolled in the reeling mill; and

Figure 3 shows schematically a cross section of a pipe being rolled in a plug mill prior to the reeling mill.

[0014] One preferred embodiment of this invention is now described specifically by reference to the accompanying drawings. Figure 1 is a block diagram showing the control system as used in a reeling mill. Figure 2 is a schematic representation of a cross section of a pipe being rolled in the reeling mill. As shown, a pipe 3 is rolled by a pair of barrel-shaped reeling rolls 6, 6 (the longitudinal axes of which cross each other) and a reeling plug 7. As the rolls and plug rotate to the directions indicated by the arrows, the reduction in the wall thickness is performed. As a result, the thickness deviation and flaws such as abrasions caused by the plug in the preceding rolling are eliminated. In the Figures are shown a guide shoe 1 that regulates the vertical position of the pipe 3, a plug bar 8 of the plug 7, a screw 9 attached to the shafts of the rolls 6, 6 for controlling the roll gap, a screw down motor 10 for operating the screw 9, and a rolling motor 12 that rotates the rolls 6, 6. In the reeling step, the greater part of the amount of reduction in wall thickness is converted into the expansion of the outside diameter of the pipe, so it is necessary to control the amount of reduction in wall thickness for the purpose of controlling the outside diameter of the pipe that leaves the reeling mill.

[0015] To know the relation between the amount of reduction in wall thickness and the expansion of the outside diameter of the pipe, we have analyzed many data that were obtained by our reeling operations, and have found that the desired amount of reduction in wall thickness (Δtq) can be determined by the following formula (1):

Δt_o: the desired amount of reduction in wall thickness;

D_R: the desired outside diameter of the reeled pipe (constant in longitudinal direction);

Dp: the actual outside diameter of pipe leaving the plug mill (OD pattern in longitudinal direction); and

tp: the average wall thickness of the pipe leaving the plug mill.

[0016] In the formula, the value of a is determined for the dimensions of a specific pipe and the kind of the steel. By using this formula one can determine optimum amount of screwing down the reeling rolls for attaining the desired outside diameter of the leaving pipe (D_R) even if the outside diameter of the incoming pipe (Dp) varies in the longitudinal direction of the pipe.

[0017] The method of determining the outside diameter of the pipe leaving the plug mill (Dp) and its average wall thickness (tp) is described below.

Outside diameter of the pipe leaving the plug mill (Dp);

[0018] The outside diameter at various points in the longitudinal direction of the pipe leaving the plug mill is calculated by the following formula (2) from the shape of the caliber formed by upper and lower rolls in the plug mill (as indicated by 2 and 5 in Figure 3), the roll gap G, and the rolling load P for the operation of the plug mill. The formula (3) can be easily obtained from Figure 3 wherein a rolling plug is indicated by 4.

wherein Go is a reference roll gap, M is the mill rigidity of the plug mill, r, is the radius of the bottom of the caliber, r₂ is the radius of the flange of the caliber, θ₁ is the angle of a sector having a radius r₁, and 8₂ is the angle of a sector having a radius r₂.

[0019] The rolling load P and roll gap G vary not only for each pipe but also in the longitudinal direction of the same pipe being rolled, so they are the factors that cause a change in the outside diameter in longitudinal direction of the pipe leaving the plug mill. The leading and trailing low-temperature ends of the pipe being fed into the plug mill are placed under a rolling load significantly higher than the one applied to the middle of the pipe, so the difference between the outside diameter of the leading and trailing ends and that of the middle portion is not negligible.

[0020] The outside diameter of the pipe leaving the plug mill can be obtained directly without using the formula (2). In the direct method, the outside diameter of the pipe leaving the plug mill or coming into the reeling mill is measured continuously in the longitudinal direction by an OD measuring instrument. The average outside diameter of the pipe leaving the plug mill (Dp) that is mentioned hereunder is determined by averaging the respective values of the outside diameter measured at various points of the pipe in the longitudinal direction. The data of D_P is fed into the AGC means 15 (Figure 1) as information on the outside diameter of the pipe on the entry side of the reeling mill.

[0021] Average wall thickness of the pipe leaving the plug mill (tp);

[0022] The average wall thickness (tp) of the pipe leaving the plug mill is determined by the following procedure. The weight of a billet is measured before it is charged into the heating furnace, the weight of the pipe in the plug mill (W) is determined by subtracting the scale loss in the heating furnace, etc., and the length of the pipe (lp) that has been rolled for the final pass in the plug mill is measured directly. The value of tp is calculated by the following formula (3) from the measurements of W, Ip and Dp:

wherein pp is the density of the steel and depends on the temperature of the steel. The data on the average wall thickness (tp) is fed into the AGC means 15 as information on the wall thickness of the pipe on the entry side of the reeling mill.

[0023] On the basis of the formulas (1), (2) and (3) described above, one can determine the optimum (desired) amount of reduction in wall thickness (Δt_o) for both a specific pipe and its longitudinal direction that is necessary to attain the desired outside diameter D_R of the pipe on the leaving side of the reeling mill. Alternatively, the wall thickness (t'p) may be directly determined by pipe thickness measuring instrument as in the case of direct measurement of the outside diameter of the pipe. For this purpose, a known hot wall thickness gauge is installed on the leaving side of the plug mill, and the respective values of the wall thickness of the pipe leaving the plug mill that are obtained by continuous measurements are averaged to calculate the tp.

[0024] The actual amount of reduction in wall thickness (Δt_A) is determined from the electric power of the rolling motor in the reeling mill and the temperature of the pipe on the entry side of the reeling mill by taking into consideration the resistance to deformation. We have discovered the following formula (4) that represents the relation between the rolling torque of the rolling motor and the amount of reduction in wall thickness. The formula assumes the use of a d.c. motor.

V_a: the voltage on the armature of the rolling motor,

l_a: the current on the armature of the rolling motor,

N_M: the motor speed,

K,: resistance to deformation,

D_R: the desired OD of the pipe leaving the reeling mill,

(3,y: constants.

[0025] The resistance to deformation (K_f) is determined from the temperature of the pipe being rolled (T), carbon content of steel, etc. Many formulas have been proposed for calculation of K_f and a suitable one may be selected depending upon the need. The temperature of the pipe being is rolled the temperature of the pipe on the entry side of the reeling mill (T) that can be directly measured in longitudinal direction with a thermometer 13. Needless to say, K_f varies in the course of rolling according to the temperature pattern in the longitudinal direction of the pipe. The data on the factors described above are fed into the AGC means 15 of Figure 1 which calculates the actual amount of reduction in wall thickness At_A by the formula (4) on the basis of these data and those on l_a, V_a, N_M and T which are also fed to the AGC. The so determined actual amount of reduction in wall thickness At_A is subtracted from the desired amount of reduction in wall thickness Δt_o, and the position to which the reeling rolls are screwed down is adjusted according to the difference. The roll gap E is adjusted to E-2 (At,-At_A) by the screw down motor control means 11 (Figure 1): when Δt_A is smaller than Δtq, the gap is reduced to increase the At_A, and if At_A is larger than Δt_o, the roll gap is increased to decrease the Δt_A.

[0026] As described above, this invention provides a method for quantitative adjustment of the roll gap that has been impossible in the conventional technique.

Probability of industrial utility

[0027] The prior art technique controls the screwing down of reeling rolls without taking into consideration the change in the temperature in longitudinal direction of the pipe on the entry side of the reeling mill, so the pipe leaving the rolls does not have a uniform outside diameter in the longitudinal direction, but this problem is not encountered in the method of this invention. In particular, a pipe both ends of which have an outside diameter equal to the desired value can be produced by the method of this invention.

[0028] Some of the prior art techniques provide a reeled pipe with a constant wall thickness only by sacrificing the uniformity of the outside diameter of the pipe in its longitudinal direction, but this problem is also eliminated from the method of this invention.

[0029] The prior art technique is not capable of quantitative control of the degree by which the reeling rolls are screwed down, so depending on the dimensions of the pipe to be rolled, hunting or delay effect frequently occurs. According to this invention, the torque of the rolling motor is measured continuously to detect the actual amount of reduction in the wall thickness of the pipe at particular points of time, and so, only one value is determined for the amount of correction of the gap between the two rolls when the actual amount of reduction in wall thickness deviates from the desired amount of reduction in wall thickness. This achieves very reliable control operation without hunting or delay effect.

[0030] As described in the foregoing, the method of this invention assures the production of a seamless steel pipe of good quality whose outside diameter is equal to the desired value and which is entirely free from any flaw such as one due to the roll edges that develops during rolling in the sizing mill.

Claims

1. A method for controlling the automatic rolling of pipes in a reeling mill comprising the steps of: determining an aimed amount of reduction in wall thickness of said pipe being reeled; continuously monitoring the voltage and current supplied to a rolling motor of the reeling mill; generating correction signals based upon the aimed reduction;

continuously monitoring the speed of said rolling motor; and

adjusting the screwing-down of reeling rolls in response to said correction signals, characterized by calculating the torque of said rolling motor by a predetermined mathematical relationship of the voltage, the current and the speed of said rolling motor;

measuring the temperature of said pipe on the entry side of said reeling mill;

directly measuring the outside diameter of the pipe supplied to said reeling mill;

directly measuring the wall thickness of said pipe supplied to said reeling mill;

calculating the estimated actual reduction in wall thickness based upon a predetermined relationship of said temperatures and said torque; and

generating said correction signals based upon the relationship between the aimed reduction and said calculated actual reduction.

2. A method according to Claim 1, characterized in that the estimated actual outside diameter Dp of the pipe leaving the plug mill is calculated by the formula:

the average wall thickness tp of the pipe leaving the plug mill is calculated by the formula:

and the aimed amount of reduction in wall thickness Δt_o is calculated from the values of the estimated actual outside diameter Dp and the average wall thickness tp by the formula:

wherein

D_R=the aimed outside diameter of the pipe leaving the reeling mill,

a=the value determined for the dimensions of a specific pipe and the type of steel of which it is made,

G=roll gap,

G_o=reference roll gap,

M=the mill stiffness of the plug,

r₁=the radius of the bottom of caliber,

r₂=the radius of the flange of caliber,

θ₁=the angle of a sector having a radius r₁,

8₂=the angle of a sector having a radius r₂,

Dp=the average outside diameter of the pipe leaving the plug mill,

I_P=pipe length,

W=p_ipe weight, and

pp=steel density.

3. A method according to Claim 1, characterized in that the estimated actual amount of reduction in the wall thickness Δt_A of the pipe being rolled is calculated by the formula:

wherein

T_rq=rolling torque,

K_f=resistance to deformation, and

β, γ=constants.

4. A method according to any one of the preceding claims, characterized in that the amount by which the roll gap in the reeling mill must be corrected is represented by 2(Δt_o-Δt_A), and if At_A is smaller than Δt_o, the roll gap is reduced to increase At_A, and if Δt_A is larger than Δt_o, the roll gap is increased to reduce Δt_A wherein Δt_o=aimed amount of reduction in wall thickness, and Δt_A =estimated actual amount of reduction in wall thickness.

Ansprüche

1. Verfahren zum Steuern des automatischen Walzens von Rohren in einem Glättwalzweck, bei dem eine Zielgröße der Wanddickenreduktion des geglätteten (oder gehaspelten) Rohrs bestimmt wird,

kontinuierlich die Spannung und der Strom, die einem Walzmotor des Glättwalzwerks zugeführt werden, überwacht werden,

Korrektursignale auf der Grundlage der Zielreduktion erzeugt werden,

kontinuierlich die Drehzahl des Walzmotors überwacht wird und

die Anstellung der Glättwalzen in Abhängigkeit von den Korrektursignalen eingestellt wird, dadurch gekennzeichnet,

daß das Drehmoment des Walzmofors nach einer vorbestimmten mathematischen Beziehung von Spannung, Strom und Drehzahl des Walzmotors berechnet wird,

die Temperatur des Rohrs an der Einlaufseite des Glättwalzwerks gemessen wird,

der Außendurchmesser des dem Glättwalzwerk zugeführten Rohrs unmittelbar gemessen wird,

die Wanddicke des dem Glättwalzwerk zugeführten Rohrs unmittelbar gemessen wird,

die geschätzte tatsächliche oder Ist-Reduktion der Wanddicke auf der Grundlage einer vorbestimmten Beziehung der Temperaturen und des Drehmoments berechnet wird und die Korrektursignale auf der Grundlage der Beziehung zwischen der Zielreduktion und der berechneten Ist-Reduktion erzeugt werden.

2. Verfahren nach Anspruch 1, dadurch gekennzeichnet, daß der geschätzte tatsächliche oder Ist-Außendurchmesser Dp des aus dem Stopfenwalzwerk(Glättwalzwerk) austretenden Rohrs nach folgender Gleichung berechnet wird:

die mittlere Wanddicke tp des aus dem Stopfenwalzerk austretenden Rohrs nach folgender Gleichung berechnet wird:

und die Zielgröße der Reduktion der Wanddicke Δt_o anhand der Größen des geschätzten Ist-Außendurchmessers Dp und d der mittleren Wanddicke tp nach folgender Gleichung berechnet wird:

wobei (in obigen Gleichungen) bedeuten:

D_R=Zeilaußendurchmesser des aus dem Glättwalzwerk austretenden Rohrs;

a=für die Abmessungen eines spezifischen Rohrs und die Sorte des Stahls, aus dem das Rohr hergestellt ist, bestimmte Größe;

G=Walzspalt;

G_o=Bezugswalzspalt;

M=Walzwerksteifheit des Stopfens;

r₁=Radius des Bodens des (des unteren) Kalibers;

r₂=Radius des Flansches des Kalibers;

θ₁=Winkel eines Sektors (Kreisauschnitts) eines Radius r₁;

θ₂=Winkel eines Sektors des Radius r₂;

DP=mittlerer Außendurchmesser des aus dem Stopfenwalzwerk austretenden Rohrs;

I_P=Rohrlänge;

W=Rohrgewicht; und

pp=Stahldichte.

3. Verfahren nach Anspruch 1, dadurch gekennzeichnet, daß die geschätzte tatsächliche oder Ist-Reduktionsgröß der Wanddicke Δt_A des ausgewalzten Rohrs nach folgender Gleichung berechnet wird:

worin bedeuten:

R,q=(Aus-)Walzdrehmoment;

K_f=Widerstand gegen Verformung; und

β,γ=Konstanten.

4. Verfahren nach einem der vorhergehenden Ansprüche, dadurch gekennzeichnet, daß die Größe, um welche der Walzenspalt im Glättwalzwerk zu korrigieren ist, durch 2(Δt_o-Δt_A) repräsentiert ist, wobei dann, wenn Δt_A kleiner ist als Δt_o, der Walzspalt zur Vergrößerung von Δt_A verkleinert, und dann, wenn Δt_A größer ist als Δt_o, der Walzspalt zur Verkleinerung von Δt_A vergrößert wird, wobei bedeuten: Δt_o=Zielgröße der Wanddickenreduktion und Δt_A=geschätzte Ist-Größe der Wanddickenreduktion.

Revendications

1. Un procédé pour commander le laminage automatique de tubes dans un laminoir lisseur, comportant les étapes consistant à:

déterminer une quantité visée de réduction de l'épaisseur de paroi dudit tube en cours de lissage;

surveiller en continu la tension et le courant délivré à un moteur de laminage du laminoir lisseur;

engendrer des signaux de correction basés sur la réduction visée;

surveiller en continu la vitesse dudit moteur de laminage; et

ajuster l'abaissement des rouleaux de lissage en réponse auxdits signaux de correction, caractérisé par

le calcul de couple dudit moteur de laminage par une relation mathématique prédéterminée entre la tension, le courant et la vitesse dudit moteur de laminage;

la mesure de la température dudit tube du côté entrée dudit laminoir lisseur;

la mesure directe du diamètre extérieur du tube délivré audit laminoir lissieur;

la mesure directe de l'épaisseur de paroi dudit tube délivré audit laminoir lisseur;

le calcul de la réduction effective estimée de l'épaisseur de paroi basé sur une relation prédéterminée entre lesdits températures et ledit couple; et

la génération desdits signaux de correction sur la base de la relation entre la réduction visée et ladite réduction effective calculée.

2. Un procédé selon la revendication 1, caractérisé en ce que le diamètre extérieur effectif estimée Dp du tube quittantle laminoire est calculé par la formule:

l'épaisseur moyenne de paroi tp du tube quittant le laminoir à tampon est calculée par la formule:

et la quantité visée de réduction de l'épaisseur de paroi Δt_o est calculée à partir des valeurs du diamètre extérieur effectif estimé Dp et de l'épaisseur moyenne de paroi t_P par la formule:

dans laquelle

D_R=le diamètre extérieur visé du tube quittant le laminoir lisseur,

a=la valeur déterminée pour les dimensions d'un tube spécifique et le type d'acier dont il est fait,

G=distance entre les rouleaux,

G_o=distance de référence entre les rouleaux,

M=raideur du tampon,

r₁=le rayon du fond du calibre,

r₂=le rayon de la collerette du calibre,

θ₁=l'angle d'un secteur ayant un rayon r₁,

8₂=l'angle d'un secteur ayant un rayon r₂,

Dp=le diamètre extérieur moyen du tube quittant le laminoir à tampon,

I_P=longueur du tube,

W=poids du tube, et

pp=densité de l'acier.

3. Un procédé selon la revendication 1, caractérisé en ce que la quantité effective estimée de réduction de l'épaisseur de paroi Δt_A du tube en cours de laminage est calculée par la formule:

dans laquelle:

T,q=couple de laminage,

K_f=résistance à la déformation, et

β,γ=constantes.

4. Un procédé selon l'une quelconque des revendications précédentes, caractérisé en ce que la quantité dont l'espace entre les rouleaux dans le laminoir lisseur doit être corrigé est représentée par 2 (Δt_o-Δt_A), et, si Δt_A est inférieur à Δt_o, l'espace entre les rouleaux est réduit pour augmenter Δt_A et, si Δt_A est supérieur à Δt_o, l'espace entre les rouleaux est augmenté pour réduire At_A, Δt_o étant la quantité visée de réduction de l'épaisseur de paroi et Δt_A étant la quantité effective estimée de réduction de l'épaisseur de paroi.

Drawing